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For a more complete list, see [[Ups and downs notation#Chords and Chord Progressions]].
For a more complete list, see [[Ups and downs notation#Chords and Chord Progressions]].
==Notation ==
==Notation ==
There are a variety of ways to notate 15edo, and the choice of notation depends heavily on which rank-2 temperament or MOS scale one wishes to treat as being the "main focus" of 15edo composition.
There are a variety of ways to notate 15edo, and the choice of notation depends heavily on which temperament or scale one wishes to treat as being the "main focus" of 15edo composition.
 
===Ups and downs notation===
15edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that downsharp is equivalent to dup (double-up) and upflat is equivalent to dud (double-down).
{{Sharpness-sharp3a}}
 
[[Alternative symbols for ups and downs notation]] uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp3}}


=== Sagittal notation===
Additional notation schemes can be found at [[15edo/Notation]].
This notation uses the same sagittal sequence as EDOs [[22edo#Sagittal notation|22]] and [[29edo#Sagittal notation|29]], is a subset of the notation for [[30edo#Sagittal notation|30-EDO]], and is a superset of the notation for [[5edo#Sagittal notation|5-EDO]].


<imagemap>
=== 5edo-based notations ===
File:15-EDO_Sagittal.svg
These notations use the notes of one or two chains of 5edo as the nominals. They (except Blackwood decatonic notation) function basically the same as each other, but with notes and accidentals relabelled.
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 439 0 599 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 439 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:15-EDO_Sagittal.svg]]
</imagemap>


===Blackwood Notation (Pentatonic)===
====Ups and downs notation====
For note names, [[Kite Giedraitis]] proposes a possible alternative to heptatonic names, pentatonic names that omit B and merge E and F into a new letter, "eef" (it rhymes with leaf). Eef, like E, is a 5th above A. Eef, like F, is a 4th above C. The circle of 5ths is C G D A Eef C. Eef is written like an E, but with the bottom horizontal line going not right but left from the vertical line. Eef can be typed as ꘙ (unicode A619) or ⊧ (unicode 22A7) or 𐐆 (unicode 10406).
15edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that downsharp is equivalent to dup (double-up) and upflat is equivalent to dud (double-down).{{Sharpness-sharp3a}}[[Alternative symbols for ups and downs notation]] uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:{{Sharpness-sharp3}}


==== Blackwood "Eef" Notation ====
For note names, [[Kite Giedraitis]] proposes a possible alternative to heptatonic names. This uses pentatonic note names as opposed to heptatonic note names, and other than the intervals, is identical to ups and downs, except for replacing E/F with a letter called "eef" (it rhymes with leaf) and omitting B. Eef is written like an E, but with the bottom horizontal line going not right but left from the vertical line.  Eef can be typed as ꘙ (unicode A619) or ⊧ (unicode 22A7) or 𐐆 (unicode 10406). Eef, like E, is a 5th above A. Eef, like F, is a 4th above C. The circle of 5ths is C G D A ꘙ C.
{| class="wikitable"
{| class="wikitable"
|-
|C
|C
|^C
|^C
Line 552: Line 538:
|vꘙ
|vꘙ
|ꘙ
|ꘙ
| ^ꘙ
|^ꘙ
|vG
|vG
|G
|G
|^G
|^G
| vA
|vA
|A
|A
|^A
|^A
Line 575: Line 561:
|v5
|v5
|P5
|P5
| ^5
|^5
|v6
|v6
|P6
|P6
|}
|}
=== Blackwood Notation (Decatonic)===
*'''Decimal Version:''' Using the nominals 1-0 (with 0 representing "10"), one of the three chains of 5edo is represented by the odd numbers, the second by the even numbers, and the third by numbers with accidentals (either odd numbers with sharps, or even numbers with flats).
*'''Guitar Version:''' On a 15edo guitar, because the "perfect fourth" comes from 5edo, all of the open strings can be tuned a perfect fourth apart and still span exactly two octaves. If one starts the [[circle of fourths]] on B — B-E-A-D-G-(B) — then the open strings of the guitar can be notated as usual (E-A-D-G-B-E). However, because the circle of fourths closes at five, and does not continue to circulate through the other 10 notes of 15edo, it is necessary to use accidentals to notate intervals on the other two chains of 5edo. This notation is not particularly ideal as a basis for a staff notation (as it requires all non-5edo chords to be notated with accidentals). It is nevertheless useful because it reflects an intuitive approach to 15edo on the guitar, since 5edo provides a useful set of 3-limit landmarks (or "perfect fourths" and "perfect fifths") that can be used to navigate the fretboard. It's especially convenient for writing chord charts, where the funky accidental-laden spellings can be more or less ignored.


===Porcupine Notation (Heptatonic) ===
==== Sagittal notation====
This notation uses the same sagittal sequence as EDOs [[22edo#Sagittal notation|22]] and [[29edo#Sagittal notation|29]], is a subset of the notation for [[30edo#Sagittal notation|30-EDO]], and is a superset of the notation for [[5edo#Sagittal notation|5-EDO]].<imagemap>
File:15-EDO_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 439 0 599 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 439 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:15-EDO_Sagittal.svg]]
</imagemap>
 
==== Blackwood guitar notation ====
On a 15edo guitar, because the "perfect fourth" comes from 5edo, all of the open strings can be tuned a perfect fourth apart and still span exactly two octaves. If one starts the [[circle of fourths]] on B — B-E-A-D-G-(B) — then the open strings of the guitar can be notated as usual (E-A-D-G-B-E). However, because the circle of fourths closes at five, and does not continue to circulate through the other 10 notes of 15edo, it is necessary to use accidentals to notate intervals on the other two chains of 5edo. This notation is not particularly ideal as a basis for a staff notation (as it requires all non-5edo chords to be notated with accidentals). It is nevertheless useful because it reflects an intuitive approach to 15edo on the guitar, since 5edo provides a useful set of 3-limit landmarks (or "perfect fourths" and "perfect fifths") that can be used to navigate the fretboard. It's especially convenient for writing chord charts, where the funky accidental-laden spellings can be more or less ignored.
 
==== Blackwood decatonic notation ====
Using the nominals 1-0 (with 0 representing "10"), one of the three chains of 5edo is represented by the odd numbers, the second by the even numbers, and the third by numbers with accidentals (either odd numbers with sharps, or even numbers with flats).
 
One can also use other systematic ways of naming nominals, such as ABC..., or use diamond-mos.
 
=== Heptatonic notations ===
 
====Porcupine Notation (Heptatonic) ====
Porcupine notation can be based on the Porcupine[7] Lssssss scale. By representing the 3|3 mode (sssLsss) with a chain of seconds (D E F G A B C D) and using sharps and flats (#/b) to denote an edostep up or down respectively, 15edo can be notated using standard notation. Its intervals can likewise be named with respect to diatonic intervals.
Porcupine notation can be based on the Porcupine[7] Lssssss scale. By representing the 3|3 mode (sssLsss) with a chain of seconds (D E F G A B C D) and using sharps and flats (#/b) to denote an edostep up or down respectively, 15edo can be notated using standard notation. Its intervals can likewise be named with respect to diatonic intervals.
{| class="wikitable"
{| class="wikitable"
|-
!Cents
!Cents
! Interval Name(s)
!Interval Name(s)
! Note name(s)
!Note name(s)
!Diamond-mos (on symmetric mode)
|-
|-
|0
|0
| Unison
|Unison
|D
|D
|J
|-
|-
| 80
|80
|Augmented Unison / Minor Second
|Augmented Unison / Minor Second
| D# / Eb
|D# / Eb
|J&/K@
|-
|-
| 160
|160
|Major Second
|Major Second
|E
|E
|K
|-
|-
| 240
|240
|Augmented Second / Diminished Third
|Augmented Second / Diminished Third
|E# / Fb
|E# / Fb
|K&/L@
|-
|-
| 320
|320
| Minor Third
|Minor Third
|F
|F
|L
|-
|-
|400
|400
| Major Third / Diminished Fourth
|Major Third / Diminished Fourth
|F# / Gb
|F# / Gb
|L&/M@
|-
|-
|480
|480
| Perfect Fourth
|Perfect Fourth
| G
|G
|M
|-
|-
|560
|560
|Augmented Fourth
|Augmented Fourth
|G#
|G#
|M&
|-
|-
|640
|640
|Diminished Fifth
|Diminished Fifth
|Ab
|Ab
|N@
|-
|-
|720
|720
|Perfect Fifth
|Perfect Fifth
| A
|A
|N
|-
|-
| 800
|800
| Augmented Fifth / Minor Sixth
|Augmented Fifth / Minor Sixth
|A# / Bb
|A# / Bb
|N&/O@
|-
|-
|880
|880
| Major Sixth
|Major Sixth
| B
|B
|O
|-
|-
|960
|960
|Augmented Sixth / Diminished Seventh
|Augmented Sixth / Diminished Seventh
|B# / Cb
|B# / Cb
|O&/P@
|-
|-
|1040
|1040
|Minor Seventh
|Minor Seventh
|C
|C
|P
|-
|-
|1120
|1120
|Major Seventh / Diminished Octave
|Major Seventh / Diminished Octave
|C# / Db
|C# / Db
|P&/J@
|-
|-
| 1200
|1200
|Octave
|Octave
| D
|D
|J
|}
|}
One neat thing about using this notation system is that its notated major scale, D E F# G A B C# D, directly corresponds to 15edo’s zarlino LH Ionian scale.


One neat thing about using this notation system is that its notated major scale, D E F# G A B C# D, directly corresponds to 15edo’s LH Nice-Ionian scale.
==== Zarlino notation (Heptatonic) ====
 
15edo's zarlino scale can also be treated as the primary scale, analogously to diatonic.
==== Zarlino notation ====
When 15edo zarlino is treated as a MODMOS of porcupine, it can also be used as nominals. Note that each interval is given a ''functional name'', since MOS-based names act unexpectedly with this as a scale:
{| class="wikitable"
{| class="wikitable"
|-
!Cents
!Cents
!Functional name
!Note name(s)
! Note name(s)
|-
|-
|0
|0
|Unison
|D
|D
|-
|-
| 80
|80
|Minor Second / Chromatic Semitone / Semitone
|D#
| D#
|-
|-
| 160
|160
|Small Wholetone
|Eb
|Eb
|-
|-
| 240
|240
|Large Wholetone / Wolf Third
|E
|E
|-
|-
| 320
|320
|Minor Third
|F
|F
|-
|-
|400
|400
|Major Third
|F#
|F#
|-
|-
|480
|480
|Augmented Third / Perfect Fourth
|Gb
| Gb
|-
|-
|560
|560
|Wolf Fourth / Diminished Fifth
|G
|G
|-
|-
|640
|640
|Wolf Fifth / Augmented Fourth
|G# / Ab
|G# / Ab
|-
|-
|720
|720
|Perfect Fifth / Diminished Sixth
|A
| A
|-
|-
| 800
|800
|Minor Sixth
|A#
|A#
|-
|-
|880
|880
|Major Sixth
|Bb
| Bb
|-
|-
|960
|960
|Harmonic Seventh / Small Minor Seventh / Wolf Sixth
|B
|B
|-
|-
|1040
|1040
|Large Minor Seventh
|C
|C
|-
|-
|1120
|1120
|Major Seventh / Diminished Octave
|C# / Db
|C# / Db
|-
|-
| 1200
|1200
|Octave
|D
| D
|}
|}


===Porcupine Notation (Octatonic)===
=== Porcupine "Quill" Notation (Octatonic) ===
Porcupine notation can also be based on the Porcupine[8] LLLLLLLs scale using eight nominals: either α β χ δ ε φ γ η or A B C D E F G H. Latin letters are easier to type and more generalizable, but they have the downside of conflicts with standard notation. Thus, Greek letters can be used in their place with a close resemblance to the spelling of ABCDEFGHA. The letters are not in greek alphabetic order.
Porcupine notation can also be based on the Porcupine[8] LLLLLLLs scale using eight nominals: either α β χ δ ε φ γ η or A B C D E F G H. Latin letters are easier to type and more generalizable, but they have the downside of conflicts with standard notation. Thus, Greek letters can be used in their place with a close resemblance to the spelling of ABCDEFGHA. The letters are not in greek alphabetic order.


The eight nominals form the base diatonic scale. In the "quill name" column, the "quill" is the name given to the two-edostep interval (160¢) of 15edo while the "small quill" (80¢) is the chroma of 15edo. This produces a very consistent notation for both Porcupine[8] and Blackwood[10], moreso than putting 15edo into a 5L 2s framework.  
The eight nominals form the base diatonic scale. In the "quill name" column, the "quill" is the name given to the two-edostep interval (160¢) of 15edo while the "small quill" (80¢) is the chroma of 15edo. This produces a very consistent notation for both Porcupine[8] and Blackwood[10], moreso than putting 15edo into a 5L 2s framework.
{| class="wikitable"
{| class="wikitable"
|-
!Cents
!Cents
!Quill Name
!Quill Name
!MOSstep Name
!MOSstep Name
! Note names (Greek)
!Note names (Greek)
!Note names (Latin)
!Note names (Latin)
|-
|-
Line 781: Line 779:
|-
|-
|480
|480
| Large Triquill
|Large Triquill
|Major 3-step
|Major 3-step
|α - δ
|α - δ
Line 793: Line 791:
|-
|-
|640
|640
| Large Fourquill
|Large Fourquill
|Major 4-step
|Major 4-step
|α - ε
|α - ε
Line 829: Line 827:
|-
|-
|1120
|1120
| Large Sevenquill
|Large Sevenquill
|Augmented 7-step
|Augmented 7-step
| α - η
|α - η
|A - H
|A - H
|-
|-
Line 840: Line 838:
|A - A
|A - A
|}
|}
A regular keyboard can be designed using this system by placing 7 black keys as Porcupine[7] and 8 whites as Porcupine[8]. In fact, [https://www.stephenweigelcomposerperformer.com/ Stephen Weigel] has already done this with his pink Halberstadt keyboard.
A regular keyboard can be designed using this system by placing 7 black keys as Porcupine[7] and 8 whites as Porcupine[8]. In fact, [https://www.stephenweigelcomposerperformer.com/ Stephen Weigel] has already done this with his pink Halberstadt keyboard.


Retrieved from "https://en.xen.wiki/w/15edo"